Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Chi-Square Wavelet Graph Neural Networks for Heterogeneous Graph Anomaly Detection

Xiping Li, Xiangyu Dong, Xingyi Zhang, Kun Xie, Yuanhao Feng, Bo Wang, Guilin Li, Wuxiong Zeng, Xiujun Shu, Sibo Wang

TL;DR

The paper tackles graph anomaly detection in heterogeneous information networks (HINs) by introducing ChiGAD, a spectral GNN framework built on a novel Chi-Square graph wavelet filter designed to capture cross-meta-path anomalies and preserve high-frequency content. ChiGAD comprises three components: Multi-Graph Chi-Square Filter for per-meta-path processing, Interactive Meta-Graph Convolution to align heterogeneous features while maintaining high-frequency information, and a Contribution-Informed Cross-Entropy Loss to emphasize difficult anomalies under class imbalance. The authors establish theoretical properties of the Chi-Square filters, including admissibility and broad spectral coverage, and demonstrate strong empirical gains on three heterogeneous datasets, with a homogeneous variant ChiGNN performing exceptionally on seven public datasets. The work advances heterogeneous GAD by enabling frequency-aware, per-meta-path learning and offers practical impact for fraud detection and other anomaly-prone, multi-typed networks; code is publicly available.

Abstract

Graph Anomaly Detection (GAD) in heterogeneous networks presents unique challenges due to node and edge heterogeneity. Existing Graph Neural Network (GNN) methods primarily focus on homogeneous GAD and thus fail to address three key issues: (C1) Capturing abnormal signal and rich semantics across diverse meta-paths; (C2) Retaining high-frequency content in HIN dimension alignment; and (C3) Learning effectively from difficult anomaly samples with class imbalance. To overcome these, we propose ChiGAD, a spectral GNN framework based on a novel Chi-Square filter, inspired by the wavelet effectiveness in diverse domains. Specifically, ChiGAD consists of: (1) Multi-Graph Chi-Square Filter, which captures anomalous information via applying dedicated Chi-Square filters to each meta-path graph; (2) Interactive Meta-Graph Convolution, which aligns features while preserving high-frequency information and incorporates heterogeneous messages by a unified Chi-Square Filter; and (3) Contribution-Informed Cross-Entropy Loss, which prioritizes difficult anomalies to address class imbalance. Extensive experiments on public and industrial datasets show that ChiGAD outperforms state-of-the-art models on multiple metrics. Additionally, its homogeneous variant, ChiGNN, excels on seven GAD datasets, validating the effectiveness of Chi-Square filters. Our code is available at https://github.com/HsipingLi/ChiGAD.

Chi-Square Wavelet Graph Neural Networks for Heterogeneous Graph Anomaly Detection

TL;DR

The paper tackles graph anomaly detection in heterogeneous information networks (HINs) by introducing ChiGAD, a spectral GNN framework built on a novel Chi-Square graph wavelet filter designed to capture cross-meta-path anomalies and preserve high-frequency content. ChiGAD comprises three components: Multi-Graph Chi-Square Filter for per-meta-path processing, Interactive Meta-Graph Convolution to align heterogeneous features while maintaining high-frequency information, and a Contribution-Informed Cross-Entropy Loss to emphasize difficult anomalies under class imbalance. The authors establish theoretical properties of the Chi-Square filters, including admissibility and broad spectral coverage, and demonstrate strong empirical gains on three heterogeneous datasets, with a homogeneous variant ChiGNN performing exceptionally on seven public datasets. The work advances heterogeneous GAD by enabling frequency-aware, per-meta-path learning and offers practical impact for fraud detection and other anomaly-prone, multi-typed networks; code is publicly available.

Abstract

Graph Anomaly Detection (GAD) in heterogeneous networks presents unique challenges due to node and edge heterogeneity. Existing Graph Neural Network (GNN) methods primarily focus on homogeneous GAD and thus fail to address three key issues: (C1) Capturing abnormal signal and rich semantics across diverse meta-paths; (C2) Retaining high-frequency content in HIN dimension alignment; and (C3) Learning effectively from difficult anomaly samples with class imbalance. To overcome these, we propose ChiGAD, a spectral GNN framework based on a novel Chi-Square filter, inspired by the wavelet effectiveness in diverse domains. Specifically, ChiGAD consists of: (1) Multi-Graph Chi-Square Filter, which captures anomalous information via applying dedicated Chi-Square filters to each meta-path graph; (2) Interactive Meta-Graph Convolution, which aligns features while preserving high-frequency information and incorporates heterogeneous messages by a unified Chi-Square Filter; and (3) Contribution-Informed Cross-Entropy Loss, which prioritizes difficult anomalies to address class imbalance. Extensive experiments on public and industrial datasets show that ChiGAD outperforms state-of-the-art models on multiple metrics. Additionally, its homogeneous variant, ChiGNN, excels on seven GAD datasets, validating the effectiveness of Chi-Square filters. Our code is available at https://github.com/HsipingLi/ChiGAD.

Paper Structure

This paper contains 31 sections, 1 theorem, 51 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. GNN-based Graph Anomaly Detection
  4. Heterogeneous Graph Learning.
  5. Preliminaries
  6. Heterogeneous Information Networks
  7. Meta-Path Graphs
  8. Dynamics of Information Diffusion
  9. Multi-Graph Filters
  10. High-frequency Area
  11. Heterogenous Graph Anomaly Detection
  12. ChiGAD
  13. Wavelet Properties of Chi-Square
  14. Multi-Graph Chi-Square Filter
  15. Interactive Meta-Graph Convolution
  16. ...and 16 more sections

Key Result

Theorem 1

For a given collection of $k$ graph signals $x_1, \cdots, x_{k}$ defined on a graph with Laplacian matrix $L$. In theory, there exists a linear alignment layer such that the aligned node representation $x_a$ perfectly keeps the $S_{high}$. Formally, $S_{high}(x_a,L)=\max\{S_{high}(x_i,L)\}_{i=1}^{k}

Figures (2)

  • Figure 1: Illustration of the ChiGAD framework, comprising three modules: (a) Multi-Graph Chi-Square Filter; (b) Interactive Meta-Graph Convolution; (c) Contribution-Informed Cross-Entropy Loss.
  • Figure 2: Comparison of results of frequency retention task across diverse alignment methods on ACM.

Theorems & Definitions (1)

  • Theorem 1